DISCRETISATIONS OF ROUGH STOCHASTIC PDES
File(s)1511.06937v2.pdf (605.75 KB)
Accepted version
Author(s)
Hairer, M
Matetski, K
Type
Journal Article
Abstract
We develop a general framework for spatial discretisations of parabolic stochastic PDEs whose solutions are provided in the framework of the theory of regularity structures and which are functions in time. As an application, we show that the dynamical $\Phi^4_3$ model on the dyadic grid converges after renormalisation to its continuous counterpart. This result in particular implies that, as expected, the $\Phi^4_3$ measure with a sufficiently small coupling constant is invariant for this equation and that the lifetime of its solutions is almost surely infinite for almost every initial condition.
Date Issued
2018-05-01
Date Acceptance
2017-07-22
Citation
ANNALS OF PROBABILITY, 2018, 46 (3), pp.1651-1709
ISSN
0091-1798
Publisher
INST MATHEMATICAL STATISTICS
Start Page
1651
End Page
1709
Journal / Book Title
ANNALS OF PROBABILITY
Volume
46
Issue
3
Copyright Statement
© The Authors
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000430923200010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
Stochastic PDEs
discretisations
regularity structures
stochastic quantization equation
invariant measure
CLASSICAL STATISTICAL-MECHANICS
QUANTUM FIELD-THEORY
DIFFERENTIAL-EQUATIONS
FINITE-VOLUME
QUANTIZATION
CONVERGENCE
MODEL
Notes
56 pages
Publication Status
Published